First-principles modeling of systems with localized d states is currently a great challenge in condensedmatter physics. Density-functional theory in the standard local-density approximation ͑LDA͒ proves to be problematic. This can be partly overcome by including local Hubbard U corrections ͑LDA+ U͒ but itinerant states are still treated on the LDA level. Many-body perturbation theory in the GW approach offers both a quasiparticle perspective ͑appropriate for itinerant states͒ and an exact treatment of exchange ͑appropriate for localized states͒, and is therefore promising for these systems. LDA+ U has previously been viewed as an approximate GW scheme. We present here a derivation that is simpler and more general, starting from the static Coulomb-hole and screened exchange approximation to the GW self-energy. Following our previous work for f-electron systems ͓H. Jiang, R. I. Gomez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 102, 126403 ͑2009͔͒ we conduct a systematic investigation of the GW method based on LDA+ U͑GW @LDA+U͒, as implemented in our recently developed all-electron GW code FHI-gap ͑Green's function with augmented plane waves͒ for a series of prototypical d-electron systems: ͑1͒ ScN with empty d states, ͑2͒ ZnS with semicore d states, and ͑3͒ late transition-metal oxides ͑MnO, FeO, CoO, and NiO͒ with partially occupied d states. We show that for ZnS and ScN, the GW band gaps only weakly depend on U but for the other transition-metal oxides the dependence on U is as strong as in LDA+ U. These different trends can be understood in terms of changes in the hybridization and screening. Our work demonstrates that GW @LDA+U with "physical" values of U provides a balanced and accurate description of both localized and itinerant states.

Many-body perturbation theory in the GW approach is applied to lanthanide oxides, using the local-density approximation plus a Hubbard U correction (LDA+U) as the starting point. Good agreement between the G0W0 density of states and experimental spectra is observed for CeO2 and Ce2O3. Unlike the LDA+U method G0W0 exhibits only a weak dependence on U in a physically meaningful range of U values. For the whole lanthanide sesquioxide (Ln2O3) series G0W0 @ LDA+U reproduces the main features found for the optical experimental band gaps. The relative positions of the occupied and unoccupied f states predicted by G0W0 confirm the experimental conjecture derived from phenomenological arguments.

The electronic structure of crystalline ZrO 2 and HfO 2 in the cubic, tetragonal, and monoclinic phase has been investigated using many-body perturbation theory in the GW approach based on density-functional theory calculations in the local-density approximation ͑LDA͒. ZrO 2 and HfO 2 are found to have very similar quasiparticle band structures. Small differences between them are already well described at the LDA level indicating that the filled f shell in HfO 2 has no significant effect on the GW corrections. A comparison with direct and inverse photoemission data shows that the GW density of states agrees very well with experiment. A systematic investigation into the structural and morphological dependence of the electronic structure reveals that the internal displacement of the oxygen atoms in the tetragonal phase has a significant effect on the band gap.

State-of-the-art theory addresses single-electron excitations in condensed matter by linking density-functional theory (DFT) with many-body perturbation theory. In actual calculations it is common to employ the pseudopotential (PP) approach, where pseudo-wave-functions enter the calculation of the self-energy, and the core-valence interaction is treated at the DFT level. In this Letter we present accurate all-electron calculations of the self-energy and systematically compare the results to those of PP calculations. The analysis for a range of different materials reveals that both above mentioned approximations are indeed problematic.

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